Phragmen's voting rules

Social choice and electoral systems
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Single-winner methods Single vote – plurality methods First preference plurality (FPP) Two-round (US: Jungle primary) Partisan primary Instant-runoff UK/NZ: Alternative vote (AV) AU: Preferential voting US/CA: Ranked-choice (RCV) Party block voting Plurality block voting Condorcet methods Condorcet-IRV Round-robin voting Minimax Kemeny Schulze Ranked pairs Maximal lottery Positional voting Plurality (el. IRV) Borda count (el. Baldwin, Mdn. Bucklin) Antiplurality (el. Coombs) Rated (cardinal) voting Score voting Approval voting Combined approval voting Majority judgment STAR voting
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Mixed systems By results of combination Mixed-member majoritarian Mixed-member proportional By mechanism of combination Non-compensatory Parallel (superposition) Coexistence Conditional Fusion (majority bonus) Compensatory Seat linkage system UK: 'AMS' NZ: 'MMP' Vote linkage system Negative vote transfer Mixed ballot Supermixed systems Dual-member mixed proportional Rural–urban proportional Majority jackpot By ballot type Single vote Double simultaneous vote Dual-vote
Paradoxes and pathologies Spoiler effects Spoiler effect Cloning paradox Frustrated majorities paradox Center squeeze Pathological response Perverse response Apportionment paradox Best-is-worst paradox No-show paradox Multiple districts paradox Strategic voting Lesser evil voting Exaggeration Truncation Turkey-raising Wasted vote Paradoxes of majority rule Tyranny of the majority Discursive dilemma Conflicting majorities paradox
Social and collective choice Impossibility theorems Arrow's theorem Majority impossibility Moulin's impossibility theorem McKelvey–Schofield chaos theorem Gibbard's theorem Positive results Median voter theorem Condorcet's jury theorem May's theorem Condorcet dominance theorems Harsanyi's utilitarian theorem Non-classical mechanisms VCG mechanism Quadratic voting Supermajority Unanimity
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Phragmén's voting rules are rules for multiwinner voting. They allow voters to vote for individual candidates rather than parties, while still guaranteeing proportional representation. They produce not only a set of candidates, but also a ranking on the set of candidates; hence, they are particularly useful for primary elections in party-list systems, where a party has to determine an ordered list of its candidates.

Phragmen's voting rules were published by Lars Edvard Phragmén in French and Swedish between 1893 and 1899, and translated to English by Svante Janson in 2016.